Teaching the Pythagorean theorem

G

gsltw

Legacy Member
Hi all,

Has anyone here taught a proof of the Pythagorean theorem a^2+b^2=c^2?

I came across this page recently that lists 104(!!) different proofs, some easier and some harder than others. Proof #3 feels particularly "nice" to me, but it requires an algebraic expansion that not all students might be familiar with. Euclid's proof (proof #1) requires no algebra (and is the most satisfying for me), but I think it's a little convoluted for presentation to students.

Of course, this is the best illustration I've seen yet:

ai.imgur.com_W8VJp.gif

How do you introduce the theorem in your class, do you try to justify it's truth to your students, and if so how do you do so?
 
Hi,

The illustration you have presented is great, this would be a fantastic resource for teaching.

It largely depends on what age you are trying to teach it to, generally I would present the formula a²+ b²= c² then something like this:
If a=3, b=4 and c=5:
awww.mathsisfun.com_geometry_images_pythagoras_3_4_5.gif
Check if the areas are the same:
32 + 42 = 52
Calculate it:
9 + 16 = 25
and say....
It works ... voila!

Now for younger tactile learners I would encourage the use of cubes or something physical to quantify each part of the calculation so they can physically move the cubes themselves, when they are comfortable they'll be making the calculations without resources in no time.
 
Hi Ferdinand,

Thanks for your response. As you pointed out in the other thread, I teach secondary (level) maths, but I was curious about how this might be introduced in really any class. My classes have students from a very wide range of backgrounds with varying amounts of prior knowledge. Above all, I'd like to see if anyone has a simple explanation of the rule - and you've hit the nail on the head there!

gs
 
The pythagorean theorem was easy for me to remember when I was going to school. It was so easy that I just did not need any techniques to use to help me remember. There are so many techniques that teachers could use. I just stuck to memorization for me.
 
That is a excellent way to show the Pythagorean theorem at work. I don't doubt that students will really like it. One of the big problems you face in class is to give a clear illustration of how things work. One thing is saying it's like that because I say so another is actually seeing it.
 
Back
Top